2. R.M.K COLLEGE OF ENGINEERING AND
TECHNOLOGY
DEPARTMENT OF ECE
EC8252-ELECTRONIC DEVICES
SECOND SEMESTER-I YEAR- (2020-2024 BATCH)
UNIT 2
Mrs.P.Sivalakshmi AP/ECE
SESSION:16
DATE: 11.05.2021
3. Hybrid II- model (Giacoletto model)
• In a Physical transistor, the charge carriers travel through Various regions of the transistor through process of drift and
diffusion. This process of diffusion causes a time delay in responding to the input signal. This delay is very small at low
frequencies and hence neglected.
• At high frequencies this delay & also capacitive effects of the transistor junctions cannot be neglected. Hence
considering this delay, the analysis of the transistor is done using high frequency model called high frequency hybrid
II- model. The parameters of the hybrid II-model almost remains constant.
Hybrid II- model of CE Transistor:-
H Parameter model of CE Transistor:-
4. Hybrid II- model of CE Transistor:-
• Node B’ represent the internal base while
node B represents the external base. The
external base is connected to the internal
base through the base spreading resistance
rbb.~100ῼ.
• rb’e =resistance between the virtual base B’
and the emitter terminal E ~1Kῼ.
• Input resistance from base to emitter with the
output short circuited is r bb’ + r b’e =h ie;
h ie = r bb’ + rb’e
• r b’c = resistance between the virtual base B’ and the collector terminal C whose typical value is 4 M ῼ.
• Cb’e =diffusion capacitance of the normally forward biased base emitter junction.~100pF.
• Cb’c = transistor capacitance of the normally reverse biased collector –base junction. It has a typical Value of
3pF.
• rce =Output resistance with typical value of 80K ῼ. If load resistance RL connected –rce can be neglected.
• gmV b’e =Output current generator value where gm is the transconductance of the transistor.
5. Hybrid 𝜫 𝑪𝒐𝒏𝒅𝒖𝒄𝒕𝒂𝒏𝒄𝒆𝒔
As the hybrid-π model is drawn for low frequencies,
the capacitive elements are considered as open
circuit.
Base Spreading Resistance (rbb’)
In the circuit shown in Fig. the value of input resistance is equal to hie when the output
terminals are short circuited i.e.,Vce = 0. Under these conditions, for the circuit in Fig.
the input impedance is given by
Zi | v ce = 0 = rbb’ + r b’e || rb’c
Therefore, hie = rbb’ + rb’e || rb’c
As r b’c > > rb’e the above equation can be written as
hie = rbb’ + rb’e
6. Conductance between terminals B’ and C or the feedback conductance (g b’c)
In the circuit show in Fig., if the input terminals are open-circuited, then the reserves
Voltage gain hre can be written for the circuit shown in Fig., and it is given by
hre = ( Vb’e / Vce ) = [rb’e / (rb’e + rb’c ) ]
Rearranging the above equation, we get rb’e (1- hre) = hre rb’c
As the value of hre is in the range of 10-4
, the above equation can be
approximated by
rb’e = hrerb’c or gb’c = hre gb’e hre = gb’c / gb’e
The equation also shows that the value of resistance rb’c is much larger than
resistance
(rb’e)i.e., rb’c > > rb’e.
7. Conductance between terminals C and E (gce)
In the circuit shown in Fig., if the input terminals are open circuited, then
Vb’e = hreVce
For the circuit in Fig. with the input terminals open i.e., Ib =0, then collector current
Ic’ is given by
Ic = Vce/rce +[ Vce/rb’e+rb’c ]+ gm Vb’e
The value of output admittance hoe is given by
hoe= Ic/Vce |Ib=0 = 1/rce + [1/rb’e +rb’c ]+gm[Vb’e/Vce ]
Substituting the value of Vb’e in the above equation, we get
hoe = 1/rce + [1/rb’e+rb’c ]+ gmhre
Assuming that rb’c >> rb’e, the above equation can be rewritten in terms of conductance as
hoe = gce+gb’c+gm [gb’c/gb’e]
Substituting gm = hƒegb’e in the equation, we get
hoe = gce+gb’c+gb’chƒe
Rearranging the terms in the above equation, we get
gce = hoe – (1+hƒe) gb’c
8. Since hƒe >> 1, the above equation can be written as
gce ≡hoe – hƒegb’c ≡ hoe – gmhƒe
Conductance between terminals B’ and E or the input conductance (gb’e)
As the value of rb’c is much greater than rb’e, most of the current Ib flows through rb’e in
the circuit shown in Fig. and the value of Vb’e is given by
Vb’e ≡ Ibrb’e
The short-circuit collector current, Ic, is given by
Ic = gm Vb’e ≡ Ibrb’e
The short-circuit current gain, hƒe, is defined as
hƒe = Ic/Ib |vct ≡ gmrb’e
Rearranging the above equation, we get
rb’e = hƒe /gm
or
gb’e = gm/ hƒe
9. Transistor’s transconductance (gm)
The transconductance of a transistor (gm) is defined as the ratio of change in Ic to change in Vb’e for
constant value of collector-emitter voltage. For common-emitter transistor configuration, the expression for
collector current is given by
Ic = ICO + αIe
The value of gm is given by
gm = ժIc/ժVb’e |vCE = constant
= α ժIe / ժVb’e = α ժIe/ ժVe
The partial derivative emitter voltage with respect to the emitter current (i.e., ժVe/ ժIe)
Can be represented as the emitter resistance (re) and the dynamic resistance of a forward-biased diode(rd)
is given as
rd = VT/ID
10. Hybrid-π Capacitances
In the hybrid-π model shown in Fig. 2.30(b), there are two capacitances, namely the collector junction barrier
capacitance (Cc) and the emitter-junction diffusion capacitance (Ce)
Collector-Junction capacitance (Cc)
The capacitance Cc is the output capacitance of the common- base transistor Configuration with the input open
(Ie = 0). As the collector-base junction is reverse-biased, Cc is the transition capacitance and it varies as (VCB)-n, where n
is ½ for abrupt junction and 1/3 for a graded junction.
Emitter-junction capacitance(Ce)
The capacitance Ce is the diffusion capacitance of the forward-biased emitter Junction and is proportional to the
emitter current Ie and is almost independent of temperature.
Where VT is the volt equivalent of temperature and ID is the diode current. Therefore, the value of gm can be
generalised as
gm = αIe/VT = Ic-Ico/VT
As Ic >>ICO, the value of gm for an NPN transistor is positive. For a PNP transistor, the analysis can be carried
out on Similar lines and the value of gm in the case of a PNP transistor is also positive. Therefor, the above
expression for
gm is written as gm = |Ic|/VT
11. Expressions of hybrid II conductance elements:-
The low frequency h-parameters for transistors are provided by manufacturers. Hence the hybrid II-parameters
can be obtained from the know h-parameters using their relationships.
The parameters of hybrid II-model are,
Transistor transconductance, gm
Input conductance, gb’e
Feedback conductance gb’c
Base-spreading resistance, rbb’
Output conductance, gce.
